A store manager set up a cardboard display to advertise a new brand of perfume. The display is a square pyramid whose base is 18 inches on each side. The height of each triangular face of a puramid is 12 inches. How much cardboard was used to make the display.
First you do Base X Height
18 x 12= 216
Because it's a squared pyramid you
divide 216 by 2
216/2 = 108. (set aside)
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Then you
Multiply 108 by 4 because there are 4 triangular faces.
108 X 4 = 432 (area of height)
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BASE IS 18 SQUARED = 324
Add the base of 324 + the height of 432 = 756 in. squared.
you have a square of side 18
and 4 triangles with base 18 and height 12.
So, since you know how to find the area of squares and triangles, just add 'em up.
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To find out how much cardboard was used to make the display, we need to calculate the surface area of the pyramid.
A square pyramid consists of a square base and four triangular faces.
First, let's calculate the area of the base:
The base of the pyramid is a square with a side length of 18 inches.
The area of a square is calculated by multiplying the length of one side by itself.
So, the area of the base is 18 inches * 18 inches = 324 square inches.
Next, let's calculate the area of each triangular face:
Each face is a right triangle with a base equal to the side length of the square base and a height of 12 inches.
The area of a triangle is calculated by multiplying the base by the height and then dividing by 2.
So, the area of each triangular face is (18 inches * 12 inches) / 2 = 108 square inches.
Since there are four triangular faces, we multiply the area of one triangular face by 4 to calculate the total area of the triangular faces:
4 * 108 square inches = 432 square inches.
Finally, to find the total surface area of the pyramid, we add the area of the base and the total area of the triangular faces:
324 square inches + 432 square inches = 756 square inches.
Therefore, 756 square inches of cardboard were used to make the display.